Principal component analysis on the floods in the UK during 1990

We decided to subset the data and focus our attention in 5 flood events that occurred in the United Kingdom during 1990. We came up with these events after slicing the Global Floods data over time and generating an animation as allowed us to perfectly tackle big and isolated flood events over time.

## Extraction of phi data

uk.floods = global.flood[c(3837,3845,3856,3924,3930),]

Transforming the data

Once the entries for the UK floods in 1990 have been located in the NOAA daily phi data, global flood records dates are transformed so that the two tables can be correctly related

uk.floods$Began <- as.numeric(as.POSIXct(as.Date(uk.floods$Began, "%d-%b-%y"), origin="1948-01-01")) %/% (24*60*60) 
uk.floods$Ended <- as.numeric(as.POSIXct(as.Date(uk.floods$Ended, "%d-%b-%y"), origin="1948-01-01")) %/% (24*60*60) 
uk.floods[,c("Began","Ended")]
##      Began Ended
## 3837  7663  7666
## 3845  7605  7607
## 3856  7583  7584
## 3924  7361  7363
## 3930  7330  7345

Using these intervals we proceeded to split the phi data into:

uk.floods.x     <- which(daily.geopot.height$X > -1)
uk.floods.y     <- which(daily.geopot.height$Y >= 45 & daily.geopot.height$Y <= 60)

interval <- function(x,y) {
  c(x - 30, y + 30)
}

uk.floods.t.1 <- interval(7663,7666)
uk.floods.t.2 <- interval(7605,7607)
uk.floods.t.3 <- interval(7583,7584)
uk.floods.t.4 <- interval(7361,7363)
uk.floods.t.5 <- interval(7330,7345)


generate_data <- function(x,y,range){

  dims <- c(length(x) * length(y), range[2]-range[1]+1)
  size <- length(x) * length(y) * (range[2]-range[1]+1)
  data <- array(1:size, dim=dims)
  j <- 1
  for (i in range[1]:range[2]){
    data[,j] <- as.vector(t(daily.geopot.height$phi[x, y, i]))
    j <- j + 1
  }
  return(data)
}

uk.floods.phi.1  <- generate_data(uk.floods.x, uk.floods.y, uk.floods.t.1)
uk.floods.phi.2  <- generate_data(uk.floods.x, uk.floods.y, uk.floods.t.2)
uk.floods.phi.3  <- generate_data(uk.floods.x, uk.floods.y, uk.floods.t.3)
uk.floods.phi.4  <- generate_data(uk.floods.x, uk.floods.y, uk.floods.t.4)
uk.floods.phi.5  <- generate_data(uk.floods.x, uk.floods.y, uk.floods.t.5)

Once we have the slices for each flood event, we ran PCA on them:

uk.floods.pca.1 <- princomp(uk.floods.phi.1, cor = TRUE, scores = TRUE)
uk.floods.pca.2 <- princomp(uk.floods.phi.2, cor = TRUE, scores = TRUE)
uk.floods.pca.3 <- princomp(uk.floods.phi.3, cor = TRUE, scores = TRUE)
uk.floods.pca.4 <- princomp(uk.floods.phi.4, cor = TRUE, scores = TRUE)
uk.floods.pca.5 <- princomp(uk.floods.phi.5, cor = TRUE, scores = TRUE)


summary(uk.floods.pca.1)
## Importance of components:
##                           Comp.1    Comp.2     Comp.3     Comp.4
## Standard deviation     5.5428126 2.9515918 2.48046518 1.82251017
## Proportion of Variance 0.4800433 0.1361233 0.09613605 0.05189911
## Cumulative Proportion  0.4800433 0.6161666 0.71230270 0.76420181
##                            Comp.5     Comp.6    Comp.7     Comp.8
## Standard deviation     1.72472263 1.34675032 1.2858591 1.16932601
## Proportion of Variance 0.04647919 0.02833963 0.0258349 0.02136443
## Cumulative Proportion  0.81068100 0.83902064 0.8648555 0.88621996
##                            Comp.9    Comp.10    Comp.11    Comp.12
## Standard deviation     1.03778324 0.97687798 0.88555546 0.83398758
## Proportion of Variance 0.01682803 0.01491079 0.01225326 0.01086774
## Cumulative Proportion  0.90304799 0.91795878 0.93021204 0.94107978
##                            Comp.13     Comp.14     Comp.15     Comp.16
## Standard deviation     0.793749748 0.626746517 0.573708158 0.524433517
## Proportion of Variance 0.009844354 0.006137675 0.005142829 0.004297352
## Cumulative Proportion  0.950924135 0.957061810 0.962204639 0.966501990
##                            Comp.17     Comp.18     Comp.19     Comp.20
## Standard deviation     0.494338471 0.467170644 0.435385818 0.412190488
## Proportion of Variance 0.003818289 0.003410131 0.002961888 0.002654703
## Cumulative Proportion  0.970320280 0.973730411 0.976692299 0.979347002
##                          Comp.21     Comp.22     Comp.23     Comp.24
## Standard deviation     0.3812821 0.337125897 0.333472773 0.307186937
## Proportion of Variance 0.0022715 0.001775842 0.001737564 0.001474435
## Cumulative Proportion  0.9816185 0.983394344 0.985131908 0.986606342
##                            Comp.25     Comp.26     Comp.27      Comp.28
## Standard deviation     0.299800148 0.279972984 0.263207732 0.2478024447
## Proportion of Variance 0.001404377 0.001224764 0.001082474 0.0009594696
## Cumulative Proportion  0.988010719 0.989235483 0.990317957 0.9912774261
##                             Comp.29      Comp.30      Comp.31      Comp.32
## Standard deviation     0.2354442700 0.2269615887 0.2136297658 0.2038270777
## Proportion of Variance 0.0008661563 0.0008048682 0.0007130887 0.0006491481
## Cumulative Proportion  0.9921435824 0.9929484506 0.9936615393 0.9943106874
##                             Comp.33      Comp.34      Comp.35      Comp.36
## Standard deviation     0.1812106128 0.1779718986 0.1686612915 0.1664002714
## Proportion of Variance 0.0005130826 0.0004949062 0.0004444786 0.0004326414
## Cumulative Proportion  0.9948237700 0.9953186762 0.9957631548 0.9961957962
##                             Comp.37     Comp.38      Comp.39      Comp.40
## Standard deviation     0.1540856670 0.149071141 0.1392531748 0.1299883254
## Proportion of Variance 0.0003709749 0.000347222 0.0003029914 0.0002640151
## Cumulative Proportion  0.9965667711 0.996913993 0.9972169844 0.9974809995
##                             Comp.41      Comp.42      Comp.43      Comp.44
## Standard deviation     0.1269949048 0.1227905374 0.1148577325 0.1111628327
## Proportion of Variance 0.0002519954 0.0002355862 0.0002061297 0.0001930809
## Cumulative Proportion  0.9977329949 0.9979685811 0.9981747107 0.9983677916
##                             Comp.45      Comp.46      Comp.47      Comp.48
## Standard deviation     0.1058692382 0.1026929396 0.0967983997 0.0959115396
## Proportion of Variance 0.0001751296 0.0001647787 0.0001464052 0.0001437347
## Cumulative Proportion  0.9985429212 0.9987077000 0.9988541051 0.9989978399
##                            Comp.49      Comp.50      Comp.51      Comp.52
## Standard deviation     0.086068640 0.0851839751 7.896836e-02 7.612013e-02
## Proportion of Variance 0.000115747 0.0001133798 9.743754e-05 9.053553e-05
## Cumulative Proportion  0.999113587 0.9992269667 9.993244e-01 9.994149e-01
##                             Comp.53      Comp.54      Comp.55      Comp.56
## Standard deviation     7.224699e-02 6.711442e-02 6.429725e-02 6.041894e-02
## Proportion of Variance 8.155668e-05 7.038039e-05 6.459587e-05 5.703826e-05
## Cumulative Proportion  9.994965e-01 9.995669e-01 9.996315e-01 9.996885e-01
##                             Comp.57      Comp.58      Comp.59      Comp.60
## Standard deviation     5.883503e-02 5.714398e-02 5.446225e-02 5.186803e-02
## Proportion of Variance 5.408688e-05 5.102241e-05 4.634588e-05 4.203583e-05
## Cumulative Proportion  9.997426e-01 9.997936e-01 9.998400e-01 9.998820e-01
##                             Comp.61      Comp.62      Comp.63      Comp.64
## Standard deviation     4.943895e-02 4.550653e-02 0.0405321416 3.733581e-02
## Proportion of Variance 3.819078e-05 3.235694e-05 0.0000256696 2.178066e-05
## Cumulative Proportion  9.999202e-01 9.999525e-01 0.9999782193 1.000000e+00
plot(uk.floods.pca.1,type = "l")

biplot(uk.floods.pca.1)

summary(uk.floods.pca.2)
## Importance of components:
##                           Comp.1    Comp.2     Comp.3     Comp.4
## Standard deviation     5.7914986 2.5766337 2.03315372 1.68693923
## Proportion of Variance 0.5324041 0.1053816 0.06561451 0.04517086
## Cumulative Proportion  0.5324041 0.6377857 0.70340018 0.74857103
##                            Comp.5     Comp.6     Comp.7     Comp.8
## Standard deviation     1.55516019 1.45535431 1.31504182 1.18106522
## Proportion of Variance 0.03838926 0.03361994 0.02744976 0.02214151
## Cumulative Proportion  0.78696029 0.82058023 0.84802999 0.87017150
##                            Comp.9    Comp.10   Comp.11   Comp.12
## Standard deviation     1.13926441 1.10797992 0.9446200 0.8662195
## Proportion of Variance 0.02060196 0.01948602 0.0141636 0.0119101
## Cumulative Proportion  0.89077346 0.91025948 0.9244231 0.9363332
##                            Comp.13     Comp.14     Comp.15    Comp.16
## Standard deviation     0.672704884 0.647042660 0.599396769 0.56264156
## Proportion of Variance 0.007183045 0.006645464 0.005702801 0.00502485
## Cumulative Proportion  0.943516229 0.950161693 0.955864494 0.96088934
##                            Comp.17     Comp.18     Comp.19     Comp.20
## Standard deviation     0.534804998 0.509096026 0.479531260 0.434310933
## Proportion of Variance 0.004539943 0.004113949 0.003650004 0.002994063
## Cumulative Proportion  0.965429286 0.969543235 0.973193239 0.976187302
##                            Comp.21     Comp.22     Comp.23     Comp.24
## Standard deviation     0.429494503 0.399321329 0.385714730 0.344945671
## Proportion of Variance 0.002928024 0.002531072 0.002361521 0.001888691
## Cumulative Proportion  0.979115326 0.981646398 0.984007920 0.985896610
##                            Comp.25     Comp.26     Comp.27     Comp.28
## Standard deviation     0.307808131 0.287796038 0.271133216 0.268433130
## Proportion of Variance 0.001503902 0.001314707 0.001166877 0.001143752
## Cumulative Proportion  0.987400513 0.988715220 0.989882096 0.991025848
##                            Comp.29      Comp.30     Comp.31      Comp.32
## Standard deviation     0.244780718 0.2378794578 0.220259586 0.2072855330
## Proportion of Variance 0.000951073 0.0008982006 0.000770068 0.0006820205
## Cumulative Proportion  0.991976921 0.9928751215 0.993645190 0.9943272100
##                             Comp.33      Comp.34      Comp.35      Comp.36
## Standard deviation     0.1849073918 0.1727819699 0.1711256422 0.1551283133
## Proportion of Variance 0.0005427102 0.0004738668 0.0004648252 0.0003819809
## Cumulative Proportion  0.9948699203 0.9953437871 0.9958086122 0.9961905931
##                             Comp.37      Comp.38      Comp.39      Comp.40
## Standard deviation     0.1514736283 0.1457754718 0.1425389311 0.1362243222
## Proportion of Variance 0.0003641946 0.0003373093 0.0003224976 0.0002945566
## Cumulative Proportion  0.9965547877 0.9968920970 0.9972145946 0.9975091512
##                             Comp.41      Comp.42      Comp.43      Comp.44
## Standard deviation     0.1271351193 0.1256545841 0.1179316034 0.1115743787
## Proportion of Variance 0.0002565609 0.0002506202 0.0002207597 0.0001976007
## Cumulative Proportion  0.9977657121 0.9980163324 0.9982370921 0.9984346928
##                            Comp.45      Comp.46      Comp.47      Comp.48
## Standard deviation     0.106734975 0.1004459134 0.0967299238 0.0952466223
## Proportion of Variance 0.000180831 0.0001601489 0.0001485187 0.0001439987
## Cumulative Proportion  0.998615524 0.9987756727 0.9989241914 0.9990681901
##                             Comp.49      Comp.50      Comp.51      Comp.52
## Standard deviation     0.0880635999 0.0838067008 0.0803390640 7.748467e-02
## Proportion of Variance 0.0001230984 0.0001114851 0.0001024502 9.529959e-05
## Cumulative Proportion  0.9991912885 0.9993027736 0.9994052239 9.995005e-01
##                             Comp.53     Comp.54      Comp.55      Comp.56
## Standard deviation     6.873348e-02 0.063771771 5.972640e-02 5.899985e-02
## Proportion of Variance 7.498875e-05 0.000064553 5.662291e-05 5.525368e-05
## Cumulative Proportion  9.995755e-01 0.999640065 9.996967e-01 9.997519e-01
##                             Comp.57      Comp.58      Comp.59      Comp.60
## Standard deviation     5.587238e-02 5.239672e-02 5.083849e-02 4.678487e-02
## Proportion of Variance 4.955116e-05 4.357803e-05 4.102463e-05 3.474325e-05
## Cumulative Proportion  9.998015e-01 9.998451e-01 9.998861e-01 9.999208e-01
##                             Comp.61      Comp.62      Comp.63
## Standard deviation     4.334473e-02 0.0419344749 3.674080e-02
## Proportion of Variance 2.982168e-05 0.0000279127 2.142677e-05
## Cumulative Proportion  9.999507e-01 0.9999785732 1.000000e+00
plot(uk.floods.pca.2,type = "l")

biplot(uk.floods.pca.2)

summary(uk.floods.pca.3)
## Importance of components:
##                           Comp.1    Comp.2     Comp.3     Comp.4
## Standard deviation     5.2938692 2.6580452 2.25340883 2.02650892
## Proportion of Variance 0.4520169 0.1139549 0.08190083 0.06623772
## Cumulative Proportion  0.4520169 0.5659719 0.64787268 0.71411040
##                            Comp.5     Comp.6     Comp.7     Comp.8
## Standard deviation     1.67438048 1.56755744 1.37654757 1.28550769
## Proportion of Variance 0.04521855 0.03963284 0.03056263 0.02665371
## Cumulative Proportion  0.75932895 0.79896179 0.82952442 0.85617813
##                            Comp.9    Comp.10    Comp.11    Comp.12
## Standard deviation     1.20545766 1.15035126 0.93005447 0.85195612
## Proportion of Variance 0.02343755 0.02134368 0.01395163 0.01170692
## Cumulative Proportion  0.87961568 0.90095936 0.91491100 0.92661792
##                            Comp.13     Comp.14     Comp.15     Comp.16
## Standard deviation     0.741437580 0.679919411 0.651188725 0.644603034
## Proportion of Variance 0.008866608 0.007456297 0.006839464 0.006701824
## Cumulative Proportion  0.935484528 0.942940824 0.949780288 0.956482112
##                            Comp.17     Comp.18     Comp.19     Comp.20
## Standard deviation     0.584597568 0.538380162 0.499047712 0.481103591
## Proportion of Variance 0.005512166 0.004675052 0.004016913 0.003733237
## Cumulative Proportion  0.961994278 0.966669330 0.970686243 0.974419480
##                            Comp.21     Comp.22     Comp.23    Comp.24
## Standard deviation     0.423923375 0.409626402 0.362209281 0.35062511
## Proportion of Variance 0.002898565 0.002706351 0.002116057 0.00198287
## Cumulative Proportion  0.977318045 0.980024396 0.982140454 0.98412332
##                            Comp.25     Comp.26     Comp.27     Comp.28
## Standard deviation     0.314139557 0.298218180 0.292358284 0.275495982
## Proportion of Variance 0.001591672 0.001434421 0.001378603 0.001224162
## Cumulative Proportion  0.985714996 0.987149417 0.988528019 0.989752181
##                            Comp.29     Comp.30      Comp.31      Comp.32
## Standard deviation     0.265092498 0.252704834 0.2328552340 0.2261129049
## Proportion of Variance 0.001133452 0.001029996 0.0008745413 0.0008246298
## Cumulative Proportion  0.990885633 0.991915629 0.9927901704 0.9936148002
##                             Comp.33      Comp.34      Comp.35      Comp.36
## Standard deviation     0.1942658611 0.1795607865 0.1724554016 0.1658891648
## Proportion of Variance 0.0006086972 0.0005200335 0.0004796914 0.0004438583
## Cumulative Proportion  0.9942234973 0.9947435308 0.9952232222 0.9956670805
##                             Comp.37      Comp.38      Comp.39      Comp.40
## Standard deviation     0.1607241976 0.1572177236 0.1510054183 0.1465683292
## Proportion of Variance 0.0004166495 0.0003986679 0.0003677845 0.0003464883
## Cumulative Proportion  0.9960837300 0.9964823979 0.9968501824 0.9971966707
##                             Comp.41      Comp.42      Comp.43      Comp.44
## Standard deviation     0.1418071591 0.1365331380 0.1246291368 0.1140609925
## Proportion of Variance 0.0003243431 0.0003006661 0.0002505229 0.0002098373
## Cumulative Proportion  0.9975210138 0.9978216799 0.9980722028 0.9982820400
##                             Comp.45      Comp.46      Comp.47      Comp.48
## Standard deviation     0.1071221862 0.1023465376 0.0981430711 0.0961575403
## Proportion of Variance 0.0001850833 0.0001689486 0.0001553558 0.0001491334
## Cumulative Proportion  0.9984671233 0.9986360719 0.9987914278 0.9989405612
##                             Comp.49      Comp.50    Comp.51      Comp.52
## Standard deviation     0.0936399679 0.0864824739 0.08435851 0.0810879961
## Proportion of Variance 0.0001414265 0.0001206326 0.00011478 0.0001060526
## Cumulative Proportion  0.9990819877 0.9992026203 0.99931740 0.9994234529
##                             Comp.53      Comp.54      Comp.55      Comp.56
## Standard deviation     0.0760095490 7.571987e-02 7.126708e-02 0.0644860568
## Proportion of Variance 0.0000931847 9.247579e-05 8.191931e-05 0.0000670718
## Cumulative Proportion  0.9995166376 9.996091e-01 9.996910e-01 0.9997581045
##                             Comp.57      Comp.58      Comp.59      Comp.60
## Standard deviation     6.257980e-02 5.481935e-02 4.892527e-02 4.664822e-02
## Proportion of Variance 6.316501e-05 4.847035e-05 3.860778e-05 3.509768e-05
## Cumulative Proportion  9.998213e-01 9.998697e-01 9.999083e-01 9.999434e-01
##                             Comp.61     Comp.62
## Standard deviation     4.245669e-02 0.041277379
## Proportion of Variance 2.907372e-05 0.000027481
## Cumulative Proportion  9.999725e-01 1.000000000
plot(uk.floods.pca.3,type = "l")

biplot(uk.floods.pca.3)

summary(uk.floods.pca.4)
## Importance of components:
##                           Comp.1    Comp.2    Comp.3     Comp.4     Comp.5
## Standard deviation     4.7869281 3.1080861 2.7410716 2.19377798 1.98965968
## Proportion of Variance 0.3637251 0.1533365 0.1192615 0.07639146 0.06283723
## Cumulative Proportion  0.3637251 0.5170616 0.6363231 0.71271453 0.77555176
##                            Comp.6     Comp.7     Comp.8     Comp.9
## Standard deviation     1.69507822 1.56778212 1.16863526 1.09341065
## Proportion of Variance 0.04560778 0.03901493 0.02167791 0.01897693
## Cumulative Proportion  0.82115954 0.86017447 0.88185238 0.90082932
##                           Comp.10    Comp.11     Comp.12    Comp.13
## Standard deviation     0.97608289 0.86254198 0.770816241 0.71321559
## Proportion of Variance 0.01512282 0.01180919 0.009431074 0.00807423
## Cumulative Proportion  0.91595214 0.92776132 0.937192399 0.94526663
##                            Comp.14     Comp.15     Comp.16     Comp.17
## Standard deviation     0.662687770 0.622374403 0.593903068 0.538138908
## Proportion of Variance 0.006970716 0.006148411 0.005598744 0.004596722
## Cumulative Proportion  0.952237344 0.958385756 0.963984499 0.968581221
##                            Comp.18     Comp.19     Comp.20     Comp.21
## Standard deviation     0.523684033 0.420935441 0.414724004 0.389568484
## Proportion of Variance 0.004353095 0.002812486 0.002730095 0.002408946
## Cumulative Proportion  0.972934316 0.975746802 0.978476898 0.980885844
##                            Comp.22     Comp.23    Comp.24     Comp.25
## Standard deviation     0.351435583 0.334014483 0.31105329 0.303903045
## Proportion of Variance 0.001960428 0.001770884 0.00153578 0.001465985
## Cumulative Proportion  0.982846272 0.984617156 0.98615294 0.987618921
##                            Comp.26     Comp.27      Comp.28      Comp.29
## Standard deviation     0.288710201 0.268304049 0.2473686122 0.2428001108
## Proportion of Variance 0.001323073 0.001142652 0.0009712894 0.0009357443
## Cumulative Proportion  0.988941993 0.990084645 0.9910559346 0.9919916790
##                             Comp.30      Comp.31      Comp.32      Comp.33
## Standard deviation     0.2227578186 0.2056951515 0.2035116813 0.1896102211
## Proportion of Variance 0.0007876356 0.0006715952 0.0006574128 0.0005706672
## Cumulative Proportion  0.9927793146 0.9934509098 0.9941083226 0.9946789898
##                             Comp.34      Comp.35      Comp.36      Comp.37
## Standard deviation     0.1788091235 0.1732990919 0.1635975222 0.1578360999
## Proportion of Variance 0.0005075032 0.0004767075 0.0004248278 0.0003954323
## Cumulative Proportion  0.9951864930 0.9956632006 0.9960880283 0.9964834606
##                             Comp.38      Comp.39      Comp.40      Comp.41
## Standard deviation     0.1510721125 0.1353475422 0.1338550089 0.1255108249
## Proportion of Variance 0.0003622664 0.0002907771 0.0002843994 0.0002500471
## Cumulative Proportion  0.9968457270 0.9971365041 0.9974209035 0.9976709506
##                             Comp.42      Comp.43      Comp.44      Comp.45
## Standard deviation     0.1193761716 0.1162381718 0.1150479880 0.1066346176
## Proportion of Variance 0.0002262011 0.0002144653 0.0002100959 0.0001804911
## Cumulative Proportion  0.9978971518 0.9981116170 0.9983217129 0.9985022040
##                             Comp.46      Comp.47      Comp.48     Comp.49
## Standard deviation     0.1006978758 0.0988381641 0.0937515086 0.091193835
## Proportion of Variance 0.0001609534 0.0001550632 0.0001395134 0.000132005
## Cumulative Proportion  0.9986631574 0.9988182206 0.9989577340 0.999089739
##                             Comp.50      Comp.51    Comp.52      Comp.53
## Standard deviation     0.0874813180 0.0824329058 0.07918977 7.687006e-02
## Proportion of Variance 0.0001214759 0.0001078601 0.00009954 9.379376e-05
## Cumulative Proportion  0.9992112149 0.9993190750 0.99941862 9.995124e-01
##                             Comp.54      Comp.55      Comp.56      Comp.57
## Standard deviation     6.894398e-02 6.681377e-02 6.445607e-02 6.138645e-02
## Proportion of Variance 7.544878e-05 7.085841e-05 6.594579e-05 5.981422e-05
## Cumulative Proportion  9.995879e-01 9.996587e-01 9.997247e-01 9.997845e-01
##                             Comp.58      Comp.59      Comp.60      Comp.61
## Standard deviation     5.706758e-02 5.158880e-02 4.604085e-02 4.480615e-02
## Proportion of Variance 5.169378e-05 4.224451e-05 3.364698e-05 3.186652e-05
## Cumulative Proportion  9.998362e-01 9.998784e-01 9.999121e-01 9.999439e-01
##                             Comp.62      Comp.63
## Standard deviation     4.385092e-02 4.012042e-02
## Proportion of Variance 3.052228e-05 2.554997e-05
## Cumulative Proportion  9.999745e-01 1.000000e+00
plot(uk.floods.pca.4,type = "l")

biplot(uk.floods.pca.4)

summary(uk.floods.pca.5)
## Importance of components:
##                           Comp.1    Comp.2    Comp.3     Comp.4     Comp.5
## Standard deviation     5.5246005 3.3717505 2.8793219 2.34074667 2.07905339
## Proportion of Variance 0.4015949 0.1495882 0.1090855 0.07209336 0.05687451
## Cumulative Proportion  0.4015949 0.5511831 0.6602685 0.73236187 0.78923639
##                            Comp.6     Comp.7     Comp.8     Comp.9
## Standard deviation     1.65068186 1.46332986 1.30396168 1.20054850
## Proportion of Variance 0.03585198 0.02817545 0.02237258 0.01896469
## Cumulative Proportion  0.82508837 0.85326382 0.87563640 0.89460109
##                          Comp.10    Comp.11    Comp.12    Comp.13
## Standard deviation     1.0777961 0.93388575 0.88641449 0.84324408
## Proportion of Variance 0.0152848 0.01147556 0.01033856 0.00935606
## Cumulative Proportion  0.9098859 0.92136145 0.93170001 0.94105607
##                            Comp.14     Comp.15     Comp.16     Comp.17
## Standard deviation     0.718511388 0.676440212 0.658449589 0.590156398
## Proportion of Variance 0.006792877 0.006020676 0.005704682 0.004582692
## Cumulative Proportion  0.947848948 0.953869624 0.959574306 0.964156998
##                            Comp.18     Comp.19     Comp.20     Comp.21
## Standard deviation     0.554937996 0.536514703 0.489180764 0.452942826
## Proportion of Variance 0.004052055 0.003787474 0.003148656 0.002699437
## Cumulative Proportion  0.968209053 0.971996527 0.975145183 0.977844620
##                            Comp.22     Comp.23     Comp.24     Comp.25
## Standard deviation     0.413036486 0.371984607 0.345332244 0.340925995
## Proportion of Variance 0.002244726 0.001820691 0.001569136 0.001529349
## Cumulative Proportion  0.980089345 0.981910037 0.983479173 0.985008522
##                            Comp.26   Comp.27     Comp.28      Comp.29
## Standard deviation     0.315955870 0.3111900 0.290415031 0.2684645335
## Proportion of Variance 0.001313528 0.0012742 0.001109749 0.0009483317
## Cumulative Proportion  0.986322050 0.9875962 0.988705998 0.9896543300
##                             Comp.30      Comp.31      Comp.32      Comp.33
## Standard deviation     0.2604588689 0.2531467576 0.2421615073 0.2320105035
## Proportion of Variance 0.0008926161 0.0008432011 0.0007716078 0.0007082747
## Cumulative Proportion  0.9905469460 0.9913901471 0.9921617549 0.9928700296
##                             Comp.34      Comp.35      Comp.36      Comp.37
## Standard deviation     0.2179406924 0.2005000901 0.1992667450 0.1870008394
## Proportion of Variance 0.0006249756 0.0005289511 0.0005224636 0.0004601226
## Cumulative Proportion  0.9934950052 0.9940239563 0.9945464200 0.9950065425
##                             Comp.38      Comp.39      Comp.40      Comp.41
## Standard deviation     0.1801746263 0.1764957207 0.1678065497 0.1555696714
## Proportion of Variance 0.0004271434 0.0004098782 0.0003705137 0.0003184464
## Cumulative Proportion  0.9954336859 0.9958435640 0.9962140777 0.9965325240
##                             Comp.42      Comp.43      Comp.44     Comp.45
## Standard deviation     0.1539163970 0.1450082065 0.1382741323 0.136004342
## Proportion of Variance 0.0003117139 0.0002766761 0.0002515755 0.000243384
## Cumulative Proportion  0.9968442379 0.9971209140 0.9973724895 0.997615873
##                             Comp.46      Comp.47      Comp.48      Comp.49
## Standard deviation     0.1295787497 0.1269559002 0.1136970759 0.1104921747
## Proportion of Variance 0.0002209296 0.0002120763 0.0001700924 0.0001606384
## Cumulative Proportion  0.9978368031 0.9980488794 0.9982189718 0.9983796103
##                             Comp.50      Comp.51      Comp.52      Comp.53
## Standard deviation     0.1092435608 0.1028871606 0.1013361821 0.0972856541
## Proportion of Variance 0.0001570284 0.0001392864 0.0001351187 0.0001245329
## Cumulative Proportion  0.9985366386 0.9986759250 0.9988110437 0.9989355766
##                             Comp.54      Comp.55      Comp.56      Comp.57
## Standard deviation     0.0883929728 8.525294e-02 8.334805e-02 8.101791e-02
## Proportion of Variance 0.0001028068 9.563242e-05 9.140654e-05 8.636713e-05
## Cumulative Proportion  0.9990383834 9.991340e-01 9.992254e-01 9.993118e-01
##                             Comp.58      Comp.59      Comp.60      Comp.61
## Standard deviation     7.776973e-02 0.0714461190 6.606618e-02 6.423756e-02
## Proportion of Variance 7.958066e-05 0.0000671651 5.743078e-05 5.429557e-05
## Cumulative Proportion  9.993914e-01 0.9994585353 9.995160e-01 9.995703e-01
##                             Comp.62      Comp.63      Comp.64      Comp.65
## Standard deviation     0.0623595609 6.051724e-02 5.985591e-02 5.678850e-02
## Proportion of Variance 0.0000511673 4.818863e-05 4.714118e-05 4.243334e-05
## Cumulative Proportion  0.9996214289 9.996696e-01 9.997168e-01 9.997592e-01
##                             Comp.66      Comp.67      Comp.68      Comp.69
## Standard deviation     5.326286e-02 4.790068e-02 4.656519e-02 4.552167e-02
## Proportion of Variance 3.732805e-05 3.019047e-05 2.853049e-05 2.726609e-05
## Cumulative Proportion  9.997965e-01 9.998267e-01 9.998552e-01 9.998825e-01
##                             Comp.70      Comp.71      Comp.72      Comp.73
## Standard deviation     4.205543e-02 3.995160e-02 3.848784e-02 3.558922e-02
## Proportion of Variance 2.327183e-05 2.100171e-05 1.949098e-05 1.666569e-05
## Cumulative Proportion  9.999058e-01 9.999268e-01 9.999463e-01 9.999629e-01
##                             Comp.74      Comp.75      Comp.76
## Standard deviation     3.385418e-02 3.072409e-02 2.695704e-02
## Proportion of Variance 1.508033e-05 1.242065e-05 9.561608e-06
## Cumulative Proportion  9.999780e-01 9.999904e-01 1.000000e+00
plot(uk.floods.pca.5,type = "l")

biplot(uk.floods.pca.5)

The same analysis after standarization of the data yields:

uk.floods.phi.1.scaled <- scale(uk.floods.phi.1)
uk.floods.phi.2.scaled <- scale(uk.floods.phi.2)
uk.floods.phi.3.scaled <- scale(uk.floods.phi.3)
uk.floods.phi.4.scaled <- scale(uk.floods.phi.4)
uk.floods.phi.5.scaled <- scale(uk.floods.phi.5)

    
colMeans(uk.floods.phi.1.scaled)  # faster version of apply(scaled.dat, 2, mean)
##  [1] -1.497930e-15  1.288421e-15 -9.126160e-16  5.290562e-16 -1.110319e-15
##  [6] -1.034666e-15  1.327174e-15  1.205055e-15  1.586584e-16 -5.396986e-16
## [11] -8.948970e-20 -7.663520e-16  1.472188e-15  2.276549e-15 -2.209707e-18
## [16] -2.669960e-16 -2.867894e-15 -1.507640e-15 -1.097984e-15 -1.515412e-15
## [21]  8.691171e-17 -1.101121e-15 -1.721176e-15 -1.935573e-15 -1.231898e-15
## [26] -9.321729e-17  2.827511e-15  2.414329e-15 -8.677541e-16  2.015283e-15
## [31]  7.783539e-17  6.529341e-16  1.444501e-16 -1.038810e-15 -1.789846e-15
## [36] -1.909411e-15  2.311519e-15 -8.543788e-16 -1.544785e-15  1.656950e-15
## [41]  7.043390e-16  1.950834e-15 -5.826933e-16 -1.734211e-15  6.701266e-16
## [46]  2.480369e-15 -2.491023e-16 -2.706823e-16  1.087806e-15 -1.121258e-15
## [51] -1.056658e-16 -2.835337e-15  1.832274e-15  9.229194e-16 -1.038612e-15
## [56] -6.401956e-19 -1.410588e-15  1.232232e-15 -1.952755e-15  5.706139e-16
## [61] -1.575115e-15 -2.040572e-15 -7.092403e-17  2.345522e-15
apply(uk.floods.phi.1.scaled, 2, sd)
##  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [36] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
uk.floods.pca.1.scaled <- princomp(uk.floods.phi.1.scaled , cor = TRUE, scores = TRUE)
uk.floods.pca.2.scaled <- princomp(uk.floods.phi.2.scaled , cor = TRUE, scores = TRUE)
uk.floods.pca.3.scaled <- princomp(uk.floods.phi.3.scaled , cor = TRUE, scores = TRUE)
uk.floods.pca.4.scaled <- princomp(uk.floods.phi.4.scaled , cor = TRUE, scores = TRUE)
uk.floods.pca.5.scaled <- princomp(uk.floods.phi.5.scaled , cor = TRUE, scores = TRUE)

summary(uk.floods.pca.1.scaled)
## Importance of components:
##                           Comp.1    Comp.2     Comp.3     Comp.4
## Standard deviation     5.5428126 2.9515918 2.48046518 1.82251017
## Proportion of Variance 0.4800433 0.1361233 0.09613605 0.05189911
## Cumulative Proportion  0.4800433 0.6161666 0.71230270 0.76420181
##                            Comp.5     Comp.6    Comp.7     Comp.8
## Standard deviation     1.72472263 1.34675032 1.2858591 1.16932601
## Proportion of Variance 0.04647919 0.02833963 0.0258349 0.02136443
## Cumulative Proportion  0.81068100 0.83902064 0.8648555 0.88621996
##                            Comp.9    Comp.10    Comp.11    Comp.12
## Standard deviation     1.03778324 0.97687798 0.88555546 0.83398758
## Proportion of Variance 0.01682803 0.01491079 0.01225326 0.01086774
## Cumulative Proportion  0.90304799 0.91795878 0.93021204 0.94107978
##                            Comp.13     Comp.14     Comp.15     Comp.16
## Standard deviation     0.793749748 0.626746517 0.573708158 0.524433517
## Proportion of Variance 0.009844354 0.006137675 0.005142829 0.004297352
## Cumulative Proportion  0.950924135 0.957061810 0.962204639 0.966501990
##                            Comp.17     Comp.18     Comp.19     Comp.20
## Standard deviation     0.494338471 0.467170644 0.435385818 0.412190488
## Proportion of Variance 0.003818289 0.003410131 0.002961888 0.002654703
## Cumulative Proportion  0.970320280 0.973730411 0.976692299 0.979347002
##                          Comp.21     Comp.22     Comp.23     Comp.24
## Standard deviation     0.3812821 0.337125897 0.333472773 0.307186937
## Proportion of Variance 0.0022715 0.001775842 0.001737564 0.001474435
## Cumulative Proportion  0.9816185 0.983394344 0.985131908 0.986606342
##                            Comp.25     Comp.26     Comp.27      Comp.28
## Standard deviation     0.299800148 0.279972984 0.263207732 0.2478024447
## Proportion of Variance 0.001404377 0.001224764 0.001082474 0.0009594696
## Cumulative Proportion  0.988010719 0.989235483 0.990317957 0.9912774261
##                             Comp.29      Comp.30      Comp.31      Comp.32
## Standard deviation     0.2354442700 0.2269615887 0.2136297658 0.2038270777
## Proportion of Variance 0.0008661563 0.0008048682 0.0007130887 0.0006491481
## Cumulative Proportion  0.9921435824 0.9929484506 0.9936615393 0.9943106874
##                             Comp.33      Comp.34      Comp.35      Comp.36
## Standard deviation     0.1812106128 0.1779718986 0.1686612915 0.1664002714
## Proportion of Variance 0.0005130826 0.0004949062 0.0004444786 0.0004326414
## Cumulative Proportion  0.9948237700 0.9953186762 0.9957631548 0.9961957962
##                             Comp.37     Comp.38      Comp.39      Comp.40
## Standard deviation     0.1540856670 0.149071141 0.1392531748 0.1299883254
## Proportion of Variance 0.0003709749 0.000347222 0.0003029914 0.0002640151
## Cumulative Proportion  0.9965667711 0.996913993 0.9972169844 0.9974809995
##                             Comp.41      Comp.42      Comp.43      Comp.44
## Standard deviation     0.1269949048 0.1227905374 0.1148577325 0.1111628327
## Proportion of Variance 0.0002519954 0.0002355862 0.0002061297 0.0001930809
## Cumulative Proportion  0.9977329949 0.9979685811 0.9981747107 0.9983677916
##                             Comp.45      Comp.46      Comp.47      Comp.48
## Standard deviation     0.1058692382 0.1026929396 0.0967983997 0.0959115396
## Proportion of Variance 0.0001751296 0.0001647787 0.0001464052 0.0001437347
## Cumulative Proportion  0.9985429212 0.9987077000 0.9988541051 0.9989978399
##                            Comp.49      Comp.50      Comp.51      Comp.52
## Standard deviation     0.086068640 0.0851839751 7.896836e-02 7.612013e-02
## Proportion of Variance 0.000115747 0.0001133798 9.743754e-05 9.053553e-05
## Cumulative Proportion  0.999113587 0.9992269667 9.993244e-01 9.994149e-01
##                             Comp.53      Comp.54      Comp.55      Comp.56
## Standard deviation     7.224699e-02 6.711442e-02 6.429725e-02 6.041894e-02
## Proportion of Variance 8.155668e-05 7.038039e-05 6.459587e-05 5.703826e-05
## Cumulative Proportion  9.994965e-01 9.995669e-01 9.996315e-01 9.996885e-01
##                             Comp.57      Comp.58      Comp.59      Comp.60
## Standard deviation     5.883503e-02 5.714398e-02 5.446225e-02 5.186803e-02
## Proportion of Variance 5.408688e-05 5.102241e-05 4.634588e-05 4.203583e-05
## Cumulative Proportion  9.997426e-01 9.997936e-01 9.998400e-01 9.998820e-01
##                             Comp.61      Comp.62      Comp.63      Comp.64
## Standard deviation     4.943895e-02 4.550653e-02 0.0405321416 3.733581e-02
## Proportion of Variance 3.819078e-05 3.235694e-05 0.0000256696 2.178066e-05
## Cumulative Proportion  9.999202e-01 9.999525e-01 0.9999782193 1.000000e+00
plot(uk.floods.pca.1.scaled,type = "l")

biplot(uk.floods.pca.1.scaled)

summary(uk.floods.pca.2.scaled)
## Importance of components:
##                           Comp.1    Comp.2     Comp.3     Comp.4
## Standard deviation     5.7914986 2.5766337 2.03315372 1.68693923
## Proportion of Variance 0.5324041 0.1053816 0.06561451 0.04517086
## Cumulative Proportion  0.5324041 0.6377857 0.70340018 0.74857103
##                            Comp.5     Comp.6     Comp.7     Comp.8
## Standard deviation     1.55516019 1.45535431 1.31504182 1.18106522
## Proportion of Variance 0.03838926 0.03361994 0.02744976 0.02214151
## Cumulative Proportion  0.78696029 0.82058023 0.84802999 0.87017150
##                            Comp.9    Comp.10   Comp.11   Comp.12
## Standard deviation     1.13926441 1.10797992 0.9446200 0.8662195
## Proportion of Variance 0.02060196 0.01948602 0.0141636 0.0119101
## Cumulative Proportion  0.89077346 0.91025948 0.9244231 0.9363332
##                            Comp.13     Comp.14     Comp.15    Comp.16
## Standard deviation     0.672704884 0.647042660 0.599396769 0.56264156
## Proportion of Variance 0.007183045 0.006645464 0.005702801 0.00502485
## Cumulative Proportion  0.943516229 0.950161693 0.955864494 0.96088934
##                            Comp.17     Comp.18     Comp.19     Comp.20
## Standard deviation     0.534804998 0.509096026 0.479531260 0.434310933
## Proportion of Variance 0.004539943 0.004113949 0.003650004 0.002994063
## Cumulative Proportion  0.965429286 0.969543235 0.973193239 0.976187302
##                            Comp.21     Comp.22     Comp.23     Comp.24
## Standard deviation     0.429494503 0.399321329 0.385714730 0.344945671
## Proportion of Variance 0.002928024 0.002531072 0.002361521 0.001888691
## Cumulative Proportion  0.979115326 0.981646398 0.984007920 0.985896610
##                            Comp.25     Comp.26     Comp.27     Comp.28
## Standard deviation     0.307808131 0.287796038 0.271133216 0.268433130
## Proportion of Variance 0.001503902 0.001314707 0.001166877 0.001143752
## Cumulative Proportion  0.987400513 0.988715220 0.989882096 0.991025848
##                            Comp.29      Comp.30     Comp.31      Comp.32
## Standard deviation     0.244780718 0.2378794578 0.220259586 0.2072855330
## Proportion of Variance 0.000951073 0.0008982006 0.000770068 0.0006820205
## Cumulative Proportion  0.991976921 0.9928751215 0.993645190 0.9943272100
##                             Comp.33      Comp.34      Comp.35      Comp.36
## Standard deviation     0.1849073918 0.1727819699 0.1711256422 0.1551283133
## Proportion of Variance 0.0005427102 0.0004738668 0.0004648252 0.0003819809
## Cumulative Proportion  0.9948699203 0.9953437871 0.9958086122 0.9961905931
##                             Comp.37      Comp.38      Comp.39      Comp.40
## Standard deviation     0.1514736283 0.1457754718 0.1425389311 0.1362243222
## Proportion of Variance 0.0003641946 0.0003373093 0.0003224976 0.0002945566
## Cumulative Proportion  0.9965547877 0.9968920970 0.9972145946 0.9975091512
##                             Comp.41      Comp.42      Comp.43      Comp.44
## Standard deviation     0.1271351193 0.1256545841 0.1179316034 0.1115743787
## Proportion of Variance 0.0002565609 0.0002506202 0.0002207597 0.0001976007
## Cumulative Proportion  0.9977657121 0.9980163324 0.9982370921 0.9984346928
##                            Comp.45      Comp.46      Comp.47      Comp.48
## Standard deviation     0.106734975 0.1004459134 0.0967299238 0.0952466223
## Proportion of Variance 0.000180831 0.0001601489 0.0001485187 0.0001439987
## Cumulative Proportion  0.998615524 0.9987756727 0.9989241914 0.9990681901
##                             Comp.49      Comp.50      Comp.51      Comp.52
## Standard deviation     0.0880635999 0.0838067008 0.0803390640 7.748467e-02
## Proportion of Variance 0.0001230984 0.0001114851 0.0001024502 9.529959e-05
## Cumulative Proportion  0.9991912885 0.9993027736 0.9994052239 9.995005e-01
##                             Comp.53     Comp.54      Comp.55      Comp.56
## Standard deviation     6.873348e-02 0.063771771 5.972640e-02 5.899985e-02
## Proportion of Variance 7.498875e-05 0.000064553 5.662291e-05 5.525368e-05
## Cumulative Proportion  9.995755e-01 0.999640065 9.996967e-01 9.997519e-01
##                             Comp.57      Comp.58      Comp.59      Comp.60
## Standard deviation     5.587238e-02 5.239672e-02 5.083849e-02 4.678487e-02
## Proportion of Variance 4.955116e-05 4.357803e-05 4.102463e-05 3.474325e-05
## Cumulative Proportion  9.998015e-01 9.998451e-01 9.998861e-01 9.999208e-01
##                             Comp.61      Comp.62      Comp.63
## Standard deviation     4.334473e-02 0.0419344749 3.674080e-02
## Proportion of Variance 2.982168e-05 0.0000279127 2.142677e-05
## Cumulative Proportion  9.999507e-01 0.9999785732 1.000000e+00
plot(uk.floods.pca.2.scaled,type = "l")

biplot(uk.floods.pca.2.scaled)

summary(uk.floods.pca.3.scaled)
## Importance of components:
##                           Comp.1    Comp.2     Comp.3     Comp.4
## Standard deviation     5.2938692 2.6580452 2.25340883 2.02650892
## Proportion of Variance 0.4520169 0.1139549 0.08190083 0.06623772
## Cumulative Proportion  0.4520169 0.5659719 0.64787268 0.71411040
##                            Comp.5     Comp.6     Comp.7     Comp.8
## Standard deviation     1.67438048 1.56755744 1.37654757 1.28550769
## Proportion of Variance 0.04521855 0.03963284 0.03056263 0.02665371
## Cumulative Proportion  0.75932895 0.79896179 0.82952442 0.85617813
##                            Comp.9    Comp.10    Comp.11    Comp.12
## Standard deviation     1.20545766 1.15035126 0.93005447 0.85195612
## Proportion of Variance 0.02343755 0.02134368 0.01395163 0.01170692
## Cumulative Proportion  0.87961568 0.90095936 0.91491100 0.92661792
##                            Comp.13     Comp.14     Comp.15     Comp.16
## Standard deviation     0.741437580 0.679919411 0.651188725 0.644603034
## Proportion of Variance 0.008866608 0.007456297 0.006839464 0.006701824
## Cumulative Proportion  0.935484528 0.942940824 0.949780288 0.956482112
##                            Comp.17     Comp.18     Comp.19     Comp.20
## Standard deviation     0.584597568 0.538380162 0.499047712 0.481103591
## Proportion of Variance 0.005512166 0.004675052 0.004016913 0.003733237
## Cumulative Proportion  0.961994278 0.966669330 0.970686243 0.974419480
##                            Comp.21     Comp.22     Comp.23    Comp.24
## Standard deviation     0.423923375 0.409626402 0.362209281 0.35062511
## Proportion of Variance 0.002898565 0.002706351 0.002116057 0.00198287
## Cumulative Proportion  0.977318045 0.980024396 0.982140454 0.98412332
##                            Comp.25     Comp.26     Comp.27     Comp.28
## Standard deviation     0.314139557 0.298218180 0.292358284 0.275495982
## Proportion of Variance 0.001591672 0.001434421 0.001378603 0.001224162
## Cumulative Proportion  0.985714996 0.987149417 0.988528019 0.989752181
##                            Comp.29     Comp.30      Comp.31      Comp.32
## Standard deviation     0.265092498 0.252704834 0.2328552340 0.2261129049
## Proportion of Variance 0.001133452 0.001029996 0.0008745413 0.0008246298
## Cumulative Proportion  0.990885633 0.991915629 0.9927901704 0.9936148002
##                             Comp.33      Comp.34      Comp.35      Comp.36
## Standard deviation     0.1942658611 0.1795607865 0.1724554016 0.1658891648
## Proportion of Variance 0.0006086972 0.0005200335 0.0004796914 0.0004438583
## Cumulative Proportion  0.9942234973 0.9947435308 0.9952232222 0.9956670805
##                             Comp.37      Comp.38      Comp.39      Comp.40
## Standard deviation     0.1607241976 0.1572177236 0.1510054183 0.1465683292
## Proportion of Variance 0.0004166495 0.0003986679 0.0003677845 0.0003464883
## Cumulative Proportion  0.9960837300 0.9964823979 0.9968501824 0.9971966707
##                             Comp.41      Comp.42      Comp.43      Comp.44
## Standard deviation     0.1418071591 0.1365331380 0.1246291368 0.1140609925
## Proportion of Variance 0.0003243431 0.0003006661 0.0002505229 0.0002098373
## Cumulative Proportion  0.9975210138 0.9978216799 0.9980722028 0.9982820400
##                             Comp.45      Comp.46      Comp.47      Comp.48
## Standard deviation     0.1071221862 0.1023465376 0.0981430711 0.0961575403
## Proportion of Variance 0.0001850833 0.0001689486 0.0001553558 0.0001491334
## Cumulative Proportion  0.9984671233 0.9986360719 0.9987914278 0.9989405612
##                             Comp.49      Comp.50    Comp.51      Comp.52
## Standard deviation     0.0936399679 0.0864824739 0.08435851 0.0810879961
## Proportion of Variance 0.0001414265 0.0001206326 0.00011478 0.0001060526
## Cumulative Proportion  0.9990819877 0.9992026203 0.99931740 0.9994234529
##                             Comp.53      Comp.54      Comp.55      Comp.56
## Standard deviation     0.0760095490 7.571987e-02 7.126708e-02 0.0644860568
## Proportion of Variance 0.0000931847 9.247579e-05 8.191931e-05 0.0000670718
## Cumulative Proportion  0.9995166376 9.996091e-01 9.996910e-01 0.9997581045
##                             Comp.57      Comp.58      Comp.59      Comp.60
## Standard deviation     6.257980e-02 5.481935e-02 4.892527e-02 4.664822e-02
## Proportion of Variance 6.316501e-05 4.847035e-05 3.860778e-05 3.509768e-05
## Cumulative Proportion  9.998213e-01 9.998697e-01 9.999083e-01 9.999434e-01
##                             Comp.61     Comp.62
## Standard deviation     4.245669e-02 0.041277379
## Proportion of Variance 2.907372e-05 0.000027481
## Cumulative Proportion  9.999725e-01 1.000000000
plot(uk.floods.pca.3.scaled,type = "l")

biplot(uk.floods.pca.3.scaled)

summary(uk.floods.pca.4.scaled)
## Importance of components:
##                           Comp.1    Comp.2    Comp.3     Comp.4     Comp.5
## Standard deviation     4.7869281 3.1080861 2.7410716 2.19377798 1.98965968
## Proportion of Variance 0.3637251 0.1533365 0.1192615 0.07639146 0.06283723
## Cumulative Proportion  0.3637251 0.5170616 0.6363231 0.71271453 0.77555176
##                            Comp.6     Comp.7     Comp.8     Comp.9
## Standard deviation     1.69507822 1.56778212 1.16863526 1.09341065
## Proportion of Variance 0.04560778 0.03901493 0.02167791 0.01897693
## Cumulative Proportion  0.82115954 0.86017447 0.88185238 0.90082932
##                           Comp.10    Comp.11     Comp.12    Comp.13
## Standard deviation     0.97608289 0.86254198 0.770816241 0.71321559
## Proportion of Variance 0.01512282 0.01180919 0.009431074 0.00807423
## Cumulative Proportion  0.91595214 0.92776132 0.937192399 0.94526663
##                            Comp.14     Comp.15     Comp.16     Comp.17
## Standard deviation     0.662687770 0.622374403 0.593903068 0.538138908
## Proportion of Variance 0.006970716 0.006148411 0.005598744 0.004596722
## Cumulative Proportion  0.952237344 0.958385756 0.963984499 0.968581221
##                            Comp.18     Comp.19     Comp.20     Comp.21
## Standard deviation     0.523684033 0.420935441 0.414724004 0.389568484
## Proportion of Variance 0.004353095 0.002812486 0.002730095 0.002408946
## Cumulative Proportion  0.972934316 0.975746802 0.978476898 0.980885844
##                            Comp.22     Comp.23    Comp.24     Comp.25
## Standard deviation     0.351435583 0.334014483 0.31105329 0.303903045
## Proportion of Variance 0.001960428 0.001770884 0.00153578 0.001465985
## Cumulative Proportion  0.982846272 0.984617156 0.98615294 0.987618921
##                            Comp.26     Comp.27      Comp.28      Comp.29
## Standard deviation     0.288710201 0.268304049 0.2473686122 0.2428001108
## Proportion of Variance 0.001323073 0.001142652 0.0009712894 0.0009357443
## Cumulative Proportion  0.988941993 0.990084645 0.9910559346 0.9919916790
##                             Comp.30      Comp.31      Comp.32      Comp.33
## Standard deviation     0.2227578186 0.2056951515 0.2035116813 0.1896102211
## Proportion of Variance 0.0007876356 0.0006715952 0.0006574128 0.0005706672
## Cumulative Proportion  0.9927793146 0.9934509098 0.9941083226 0.9946789898
##                             Comp.34      Comp.35      Comp.36      Comp.37
## Standard deviation     0.1788091235 0.1732990919 0.1635975222 0.1578360999
## Proportion of Variance 0.0005075032 0.0004767075 0.0004248278 0.0003954323
## Cumulative Proportion  0.9951864930 0.9956632006 0.9960880283 0.9964834606
##                             Comp.38      Comp.39      Comp.40      Comp.41
## Standard deviation     0.1510721125 0.1353475422 0.1338550089 0.1255108249
## Proportion of Variance 0.0003622664 0.0002907771 0.0002843994 0.0002500471
## Cumulative Proportion  0.9968457270 0.9971365041 0.9974209035 0.9976709506
##                             Comp.42      Comp.43      Comp.44      Comp.45
## Standard deviation     0.1193761716 0.1162381718 0.1150479880 0.1066346176
## Proportion of Variance 0.0002262011 0.0002144653 0.0002100959 0.0001804911
## Cumulative Proportion  0.9978971518 0.9981116170 0.9983217129 0.9985022040
##                             Comp.46      Comp.47      Comp.48     Comp.49
## Standard deviation     0.1006978758 0.0988381641 0.0937515086 0.091193835
## Proportion of Variance 0.0001609534 0.0001550632 0.0001395134 0.000132005
## Cumulative Proportion  0.9986631574 0.9988182206 0.9989577340 0.999089739
##                             Comp.50      Comp.51    Comp.52      Comp.53
## Standard deviation     0.0874813180 0.0824329058 0.07918977 7.687006e-02
## Proportion of Variance 0.0001214759 0.0001078601 0.00009954 9.379376e-05
## Cumulative Proportion  0.9992112149 0.9993190750 0.99941862 9.995124e-01
##                             Comp.54      Comp.55      Comp.56      Comp.57
## Standard deviation     6.894398e-02 6.681377e-02 6.445607e-02 6.138645e-02
## Proportion of Variance 7.544878e-05 7.085841e-05 6.594579e-05 5.981422e-05
## Cumulative Proportion  9.995879e-01 9.996587e-01 9.997247e-01 9.997845e-01
##                             Comp.58      Comp.59      Comp.60      Comp.61
## Standard deviation     5.706758e-02 5.158880e-02 4.604085e-02 4.480615e-02
## Proportion of Variance 5.169378e-05 4.224451e-05 3.364698e-05 3.186652e-05
## Cumulative Proportion  9.998362e-01 9.998784e-01 9.999121e-01 9.999439e-01
##                             Comp.62      Comp.63
## Standard deviation     4.385092e-02 4.012042e-02
## Proportion of Variance 3.052228e-05 2.554997e-05
## Cumulative Proportion  9.999745e-01 1.000000e+00
plot(uk.floods.pca.4.scaled,type = "l")

biplot(uk.floods.pca.4.scaled)

summary(uk.floods.pca.5.scaled)
## Importance of components:
##                           Comp.1    Comp.2    Comp.3     Comp.4     Comp.5
## Standard deviation     5.5246005 3.3717505 2.8793219 2.34074667 2.07905339
## Proportion of Variance 0.4015949 0.1495882 0.1090855 0.07209336 0.05687451
## Cumulative Proportion  0.4015949 0.5511831 0.6602685 0.73236187 0.78923639
##                            Comp.6     Comp.7     Comp.8     Comp.9
## Standard deviation     1.65068186 1.46332986 1.30396168 1.20054850
## Proportion of Variance 0.03585198 0.02817545 0.02237258 0.01896469
## Cumulative Proportion  0.82508837 0.85326382 0.87563640 0.89460109
##                          Comp.10    Comp.11    Comp.12    Comp.13
## Standard deviation     1.0777961 0.93388575 0.88641449 0.84324408
## Proportion of Variance 0.0152848 0.01147556 0.01033856 0.00935606
## Cumulative Proportion  0.9098859 0.92136145 0.93170001 0.94105607
##                            Comp.14     Comp.15     Comp.16     Comp.17
## Standard deviation     0.718511388 0.676440212 0.658449589 0.590156398
## Proportion of Variance 0.006792877 0.006020676 0.005704682 0.004582692
## Cumulative Proportion  0.947848948 0.953869624 0.959574306 0.964156998
##                            Comp.18     Comp.19     Comp.20     Comp.21
## Standard deviation     0.554937996 0.536514703 0.489180764 0.452942826
## Proportion of Variance 0.004052055 0.003787474 0.003148656 0.002699437
## Cumulative Proportion  0.968209053 0.971996527 0.975145183 0.977844620
##                            Comp.22     Comp.23     Comp.24     Comp.25
## Standard deviation     0.413036486 0.371984607 0.345332244 0.340925995
## Proportion of Variance 0.002244726 0.001820691 0.001569136 0.001529349
## Cumulative Proportion  0.980089345 0.981910037 0.983479173 0.985008522
##                            Comp.26   Comp.27     Comp.28      Comp.29
## Standard deviation     0.315955870 0.3111900 0.290415031 0.2684645335
## Proportion of Variance 0.001313528 0.0012742 0.001109749 0.0009483317
## Cumulative Proportion  0.986322050 0.9875962 0.988705998 0.9896543300
##                             Comp.30      Comp.31      Comp.32      Comp.33
## Standard deviation     0.2604588689 0.2531467576 0.2421615073 0.2320105035
## Proportion of Variance 0.0008926161 0.0008432011 0.0007716078 0.0007082747
## Cumulative Proportion  0.9905469460 0.9913901471 0.9921617549 0.9928700296
##                             Comp.34      Comp.35      Comp.36      Comp.37
## Standard deviation     0.2179406924 0.2005000901 0.1992667450 0.1870008394
## Proportion of Variance 0.0006249756 0.0005289511 0.0005224636 0.0004601226
## Cumulative Proportion  0.9934950052 0.9940239563 0.9945464200 0.9950065425
##                             Comp.38      Comp.39      Comp.40      Comp.41
## Standard deviation     0.1801746263 0.1764957207 0.1678065497 0.1555696714
## Proportion of Variance 0.0004271434 0.0004098782 0.0003705137 0.0003184464
## Cumulative Proportion  0.9954336859 0.9958435640 0.9962140777 0.9965325240
##                             Comp.42      Comp.43      Comp.44     Comp.45
## Standard deviation     0.1539163970 0.1450082065 0.1382741323 0.136004342
## Proportion of Variance 0.0003117139 0.0002766761 0.0002515755 0.000243384
## Cumulative Proportion  0.9968442379 0.9971209140 0.9973724895 0.997615873
##                             Comp.46      Comp.47      Comp.48      Comp.49
## Standard deviation     0.1295787497 0.1269559002 0.1136970759 0.1104921747
## Proportion of Variance 0.0002209296 0.0002120763 0.0001700924 0.0001606384
## Cumulative Proportion  0.9978368031 0.9980488794 0.9982189718 0.9983796103
##                             Comp.50      Comp.51      Comp.52      Comp.53
## Standard deviation     0.1092435608 0.1028871606 0.1013361821 0.0972856541
## Proportion of Variance 0.0001570284 0.0001392864 0.0001351187 0.0001245329
## Cumulative Proportion  0.9985366386 0.9986759250 0.9988110437 0.9989355766
##                             Comp.54      Comp.55      Comp.56      Comp.57
## Standard deviation     0.0883929728 8.525294e-02 8.334805e-02 8.101791e-02
## Proportion of Variance 0.0001028068 9.563242e-05 9.140654e-05 8.636713e-05
## Cumulative Proportion  0.9990383834 9.991340e-01 9.992254e-01 9.993118e-01
##                             Comp.58      Comp.59      Comp.60      Comp.61
## Standard deviation     7.776973e-02 0.0714461190 6.606618e-02 6.423756e-02
## Proportion of Variance 7.958066e-05 0.0000671651 5.743078e-05 5.429557e-05
## Cumulative Proportion  9.993914e-01 0.9994585353 9.995160e-01 9.995703e-01
##                             Comp.62      Comp.63      Comp.64      Comp.65
## Standard deviation     0.0623595609 6.051724e-02 5.985591e-02 5.678850e-02
## Proportion of Variance 0.0000511673 4.818863e-05 4.714118e-05 4.243334e-05
## Cumulative Proportion  0.9996214289 9.996696e-01 9.997168e-01 9.997592e-01
##                             Comp.66      Comp.67      Comp.68      Comp.69
## Standard deviation     5.326286e-02 4.790068e-02 4.656519e-02 4.552167e-02
## Proportion of Variance 3.732805e-05 3.019047e-05 2.853049e-05 2.726609e-05
## Cumulative Proportion  9.997965e-01 9.998267e-01 9.998552e-01 9.998825e-01
##                             Comp.70      Comp.71      Comp.72      Comp.73
## Standard deviation     4.205543e-02 3.995160e-02 3.848784e-02 3.558922e-02
## Proportion of Variance 2.327183e-05 2.100171e-05 1.949098e-05 1.666569e-05
## Cumulative Proportion  9.999058e-01 9.999268e-01 9.999463e-01 9.999629e-01
##                             Comp.74      Comp.75      Comp.76
## Standard deviation     3.385418e-02 3.072409e-02 2.695704e-02
## Proportion of Variance 1.508033e-05 1.242065e-05 9.561608e-06
## Cumulative Proportion  9.999780e-01 9.999904e-01 1.000000e+00
plot(uk.floods.pca.5.scaled,type = "l")

biplot(uk.floods.pca.5.scaled)